Advice for an interesting 'preferred lie' scenario

Extract from the specimen rule:

"A ball lying on a closely mown area through the green (or specify a more restricted area, e.g., at the 6th hole) may be lifted, without penalty, and cleaned. Before lifting the ball, the player must mark its position. Having lifted the ball, he must place it on a spot within (specify area, e.g., six inches, one club-length, etc.) of and not nearer the hole than where it originally lay, that is not in a hazard and not on a putting green."